Thin streams of liquid commonly break up into characteristic droplet patterns owing to the surface-tension-driven Plateau–Rayleigh instability1,2,3. Very similar patterns are observed when initially uniform streams of dry granular material break up into clusters of grains4,5,6, even though flows of macroscopic particles are considered to lack surface tension7,8. Recent studies on freely falling granular streams tracked fluctuations in the stream profile9, but the clustering mechanism remained unresolved because the full evolution of the instability could not be observed. Here we demonstrate that the cluster formation is driven by minute, nanoNewton cohesive forces that arise from a combination of van der Waals interactions and capillary bridges between nanometre-scale surface asperities. Our experiments involve high-speed video imaging of the granular stream in the co-moving frame, control over the properties of the grain surfaces and the use of atomic force microscopy to measure grain–grain interactions. The cohesive forces that we measure correspond to an equivalent surface tension five orders of magnitude below that of ordinary liquids. We find that the shapes of these weakly cohesive, non-thermal clusters of macroscopic particles closely resemble droplets resulting from thermally induced rupture of liquid nanojets10,11,12.
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Shi, X. D., Brenner, M. P. & Nagel, S. R. A cascade of structure in a drop falling from a faucet. Science 265, 219–222 (1994)
Eggers, J. & Villermaux, E. Physics of liquid jets. Rep. Prog. Phys. 71, 036601, (2008)
Doshi, P. et al. Persistence of memory in drop breakup: the breakdown of universality. Science 302, 1185–1188 (2003)
Lohse, D. et al. Impact on soft sand: void collapse and jet formation. Phys. Rev. Lett. 93, 198003 (2004)
Royer, J. R. et al. Formation of granular jets observed by high-speed X-ray radiography. Nature Phys. 1, 164–167 (2005)
Möbius, M. E. Clustering instability in a freely falling granular jet. Phys. Rev. E 74, 051304 (2006)
Cheng, X., Xu, L., Patterson, A., Jaeger, H. M. & Nagel, S. R. Towards the zero-surface-tension limit in granular fingering instability. Nature Phys. 4, 234–237 (2008)
Cheng, X., Varas, G., Citron, D., Jaeger, H. M. & Nagel, S. R. Collective behavior in a granular jet: emergence of a liquid with zero surface tension. Phys. Rev. Lett. 99, 188001 (2007)
Amarouchene, Y., Boudet, J.-F. & Kellay, H. Capillarylike fluctuations at the interface of falling granular jets. Phys. Rev. Lett. 100, 218001 (2008)
Koplik, J. & Banavar, J. R. Molecular dynamics of interface rupture. Phys. Fluids A 5, 521–536 (1993)
Moseler, M. & Landman, U. Formation, stability, and breakup of nanojets. Science 289, 1165–1169 (2000)
Kawano, S. Molecular dynamics of rupture phenomena in a liquid thread. Phys. Rev. E 58, 4468–4472 (1998)
Khamontoff, N. Application of photography to the study of the structure of trickles of fluid and dry materials. J. Russ. Phys-Chem. Soc. 22, 281–284 (1890)
Goldhirsch, I. Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267–293 (2003)
Brilliantov, N. V. & Pöschel, T. Kinetic Theory of Granular Gases (Oxford University Press, 2004)
Efrati, E., Livne, E. & Meerson, B. Hydrodynamic singularities and clustering in a freely cooling inelastic gas. Phys. Rev. Lett. 94, 088001 (2005)
Kuwabara, G. & Kono, K. Restitution coefficient in a collision between two spheres. Jpn. J. Appl. Phys. 26, 1230–1233 (1987)
Foerster, S. F., Louge, M. Y., Chang, H. & Allia, K. Measurements of the collision properties of small spheres. Phys. Fluids 6, 1108–1115 (1994)
Israelachvili, J. N. Intermolecular and Surface Forces 2nd edn (Academic Press, 1992)
Podczeck, F. Particle-Particle Adhesion in Pharmaceutical Powder Handling (Imperial College Press, 1998)
Visser, J. Van der Waals and other cohesive forces affecting powder fluidization. Powder Technol. 58, 1–10 (1989)
Jones, R. From single particle AFM studies of adhesion and friction to bulk flow: forging the links. Granular Matter 4, 191–204 (2003)
Schaefer, D. M. et al. in Fundamentals of Adhesion and Interfaces (eds Rimai, D. S., Demejo, L. P. & Mittal, K. L.) 35–48 (VSP, 1995)
Halsey, T. C. & Levine, A. J. How sandcastles fall. Phys. Rev. Lett. 80, 3141–3144 (1998)
Bocquet, L., Charlaix, E., Ciliberto, S. & Crassous, J. Moisture-induced ageing in granular media and the kinetics of capillary condensation. Nature 396, 735–737 (1998)
Brilliantov, N. V., Albers, N., Spahn, F. & Pöschel, T. Collision dynamics of granular particles with adhesion. Phys. Rev. E 76, 051302 (2007)
Sorace, C. M., Louge, M. Y., Crozier, M. D. & Law, V. H. C. High apparent adhesion energy in the breakdown of normal restitution for binary impacts of small spheres at low speed. Mech. Res. Commun. 36, 364–368 (2009)
Rowlinson, J. S. & Widom, B. Molecular Theory of Capillarity (Clarendon Press, 1982)
Hennequin, Y. et al. Drop formation by thermal fluctuations at an ultralow surface tension. Phys. Rev. Lett. 97, 244502 (2006)
Eggers, J. Dynamics of liquid nanojets. Phys. Rev. Lett. 89, 084502 (2002)
We thank X. Cheng, R. Cocco, E. Corwin, R. Karri, N. Keim, T. Knowlton, S. Nagel, T. Witten and W. Zhang for discussions and J. Jureller for AFM training and assistance. This work was supported by NSF through its MRSEC programme and the Inter-American Materials Collaboration Chicago-Chile, and by the Keck Initiative for Ultrafast Imaging at the University of Chicago.
This file contains Supplementary Notes and Data, Supplementary Figures 1-4 with Legends and Supplementary References. (PDF 1966 kb)
This file shows a high-speed movie of the break up of a granular stream. The camera falls with the stream to capture the break up of a stream of d = (107 ± 19) μm diameter glass grains falling out of a D0 = 4.0 mm nozzle. The nozzle and reservoir of grains are housed in a 2.5 m tall acrylic tube, which is sealed and evacuated to 0.03 kPa (gas mean free path ~ 200 μm) to reduce air drag. (MOV 3598 kb)
This file shows a high-speed movie of a stream of d = (130 ± 30) μm diameter copper grains. Conditions are otherwise identical to those in Supplementary Movie 1. (MOV 2376 kb)
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Royer, J., Evans, D., Oyarte, L. et al. High-speed tracking of rupture and clustering in freely falling granular streams. Nature 459, 1110–1113 (2009). https://doi.org/10.1038/nature08115
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